: In complex
algebraic geometry, the notion of a multiplier ideal sheaf has played an
important role in the study of algebraic varieties of general dimension. A
multiplier ideal sheaf measures the singularity of a 'singular pole' given by
the zeros of a finite set of holomorphic functions. Also more generally, it is
natural to define the multiplier ideal sheaf of a plurisubharmonic function. In
this talk, we will discuss applications of the fundamental subadditivity
property of multiplier ideal sheaves and also of a more recent superadditivity
type result due to Popovici. We will also discuss related results stemming from
work of Lindholm and Berndtsson on Bergman kernels.